I ended up going with the Schiit Asgard-2 and the Schiit Modi. Since I made this post, I have also acquired the Mad Dogs by Mrspeakers, which I use more than the HiFiMANs. From my memory, though, the HE-400s and the Asgard-2/Modi did pretty well together.
Hey, guys, just to let you know, I won't be able to bring my laptop or my schiit stack to set up, so if you want to try any of the headphones that I'm bringing, just confront me. I'll be the 16 year old with the backpack. :P